Submission date: 26 February 2007.

Abstract:

We prove the Zil'ber Trichotomy Principle for all 1-dimensional structures which are definable in o-minimal ones. In particular, we show that any stable 1-dimensional structure is necessarily locally modular. The main tool is a theory for intersection of curves which we develop.

Mathematics Subject Classification: 03C45; 03C64

Keywords and phrases: o-minimality, Zilber's trichotomy, strongly minimal sets.

Full text: arXiv.